Direct one-step block methods for solving special second order delay differential equations

This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simult...

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Main Author:	Rasdi, Nadzirah
Format:	Thesis
Language:	English
Published:	2013
Subjects:	Delay differential equations - Numerical solutions Polynomials
Online Access:	http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf
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id	my-upm-ir.39139
record_format	uketd_dc
spelling	my-upm-ir.391392016-04-11T09:24:17Z Direct one-step block methods for solving special second order delay differential equations 2013-05 Rasdi, Nadzirah This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simultaneously at more than one point based on equidistant block method and each of these values is calculated independently of each other. In this research, the block methods are implemented based on the predictor-corrector scheme using constant step size technique. The derivation of two point, three point, extended two point and extended three point implicit block methods were also described. Those methods were derived using Lagrange interpolation polynomial. The stability polynomials for the methods are obtained and their regions of absolute stability are discussed. Subsequently, the one-step block methods were then adapted to solve delay differential equations. The basic idea is to apply the same integration method and use interpolation polynomial to approximate the solution in the previous value. The efficiency of the proposed block method is supported by some numerical results. The results showed that the block methods proposed in this thesis are suitable to solve second order DDEs. Delay differential equations - Numerical solutions Polynomials 2013-05 Thesis http://psasir.upm.edu.my/id/eprint/39139/ http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf application/pdf en public masters Universiti Putra Malaysia Delay differential equations - Numerical solutions Polynomials
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Delay differential equations - Numerical solutions Polynomials
spellingShingle	Delay differential equations - Numerical solutions Polynomials Rasdi, Nadzirah Direct one-step block methods for solving special second order delay differential equations
description	This thesis describes the implementation of one-step block methods of Runge-Kutta type for solving second order Delay Differential Equations (DDEs). The one-step block method will solve the second order DDEs directly without reducing to first order equations. The solution will be approximated simultaneously at more than one point based on equidistant block method and each of these values is calculated independently of each other. In this research, the block methods are implemented based on the predictor-corrector scheme using constant step size technique. The derivation of two point, three point, extended two point and extended three point implicit block methods were also described. Those methods were derived using Lagrange interpolation polynomial. The stability polynomials for the methods are obtained and their regions of absolute stability are discussed. Subsequently, the one-step block methods were then adapted to solve delay differential equations. The basic idea is to apply the same integration method and use interpolation polynomial to approximate the solution in the previous value. The efficiency of the proposed block method is supported by some numerical results. The results showed that the block methods proposed in this thesis are suitable to solve second order DDEs.
format	Thesis
qualification_level	Master's degree
author	Rasdi, Nadzirah
author_facet	Rasdi, Nadzirah
author_sort	Rasdi, Nadzirah
title	Direct one-step block methods for solving special second order delay differential equations
title_short	Direct one-step block methods for solving special second order delay differential equations
title_full	Direct one-step block methods for solving special second order delay differential equations
title_fullStr	Direct one-step block methods for solving special second order delay differential equations
title_full_unstemmed	Direct one-step block methods for solving special second order delay differential equations
title_sort	direct one-step block methods for solving special second order delay differential equations
granting_institution	Universiti Putra Malaysia
publishDate	2013
url	http://psasir.upm.edu.my/id/eprint/39139/1/FS%202013%2038%20IR.pdf
_version_	1747811772056731648

Direct one-step block methods for solving special second order delay differential equations

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